The present invention relates to forecasting, particularly to short to medium term weather forecasting using an ensemble, model-based approach.
Techniques for weather forecasting, which are now largely computer-based, vary depending on the timescale required for the forecast. Short term forecasts of a few days or so use computer models and can be quite accurate. As for longer timescales, such as climate forecasts on longer timescales, although individual weather events are unpredictable at lead times greater than a week or so, it is theoretically possible to make more general predictions, relating to the statistics or probability of weather events, beyond this time horizon. This is possible because there are aspects of the climate system which vary on timescales which are longer than those of individual weather events that can bias their probability of occurrence. The principal climate phenomenon which varies on timescales from seasons to years is known as the El Nino Southern Oscillation (ENSO). ENSO involves a quasi-periodic warming and cooling of the eastern tropical Pacific sea surface, and it influences both the local and remote atmospheric circulation patterns. ENSO has a widespread impact on world ecology, society and economics, and great effort is made to predict ENSO at seasonal lead times using both statistical and dynamical methods.
Statistical seasonal forecasting methods rely on predicting some index of climate variability (for example the ocean temperature anomalies in the eastern tropical Pacific—the Nino-3 index) and deducing the local and remote impacts (so-called teleconnection patterns) using canonical relationships established from prior observatiois. However, often these relationships are insufficiently accurate and result in erroneous predictions.
Dynamical methods for forecasting use coupled atmosphere-ocean global circulation computer models (AOGCM) that solve the physical equations of the system and represent the complex interactions between all aspects of the climate system. An example of such a system is that in current use at the European Centre for Medium Range Weather Forecasting. In the accompanying drawings FIG. 1 illustrates how such a computer model is used. Firstly, observations 1 of the current state of the climate system are acquired, and these are input into the model at 2 (known as assimilation) to produce a best estimate of its current state. The model is then run forward in time to produce the forecast 4. As illustrated in FIG. 1, rather than running the model once, from a single initial state, a range of different initial states is used at 3 (by perturbing the initial state given by assimilation) so that a number of forecasts are produced which are hoped to span the range of future weather states consistent with current information. This “ensemble initialization” process, though, is difficult and problematic. For instance, simply replacing variables in the model with the currently observed values results in a model state which is very different from a state the model would generate “naturally” through its own operation. Gaps and errors in the observations and models introduce discontinuities from which unrealistically large-amplitude waves propagate as soon as the forecast is launched. A wide range of techniques have been developed to assimilate data into models to initialise forecast with a reasonably balanced state, but they are time-consuming and problems remain. One problem is that the models have a base model climate (ie the mean annual cycle generated by running the model for a long time period given only the external boundary conditions on the climate system) which is different from the observed climate. This means that as soon as the forecast is launched, the model begins to drift back to its own base climate. Over a 10-day weather forecast, these drifts may be relatively unimportant. But for a seasonal time scale, the drift may be comparable or larger than the signals being forecast. Thus while such an appraoch may be useful for short term forecasting, it is more differcult to use for seasonal forecasting.
A traditional way to forecast the weather (as used in, for example, the 1950's) was to examine historical weather maps for situations which are analogous to the present conditions, referred to below as “analogs”, and then base a forecast on some weighted average of the evolution of the analog states found. This can be regarded as an example of a method known as a “perfect ensemble” which involves choosing analogs which are naturally in a state similar to the present state, and then using them for predictive purposes. However, a difficulty with this approach in weather forecasting is that the “return-time” of the atmosphere has been estimated to be of the order of many millions of years. That is to say forecasters would have to wait for this length of time before having a reasonable chance of observing a single atmospheric state consistent with the analysis on a particular day. Thus, this approach has been superseded by the use of the computer models mentioned above.
An approach to long-term climate prediction has been proposed which uses distributed computing, namely the distribution of climate models to a plurality of personal computers, in which models are allowed to run over a period from the past to the future, and those simulations which are consistent with recent observed climate change are used as the basis for ensemble forecasts of the future change. However, the climate prediction problem is fundamentally different from seasonal forecasting, because in climate prediction the main source of uncertainty lies in the response of the climate to changing boundary conditions: that is drivers such as changing levels of anthropogenic greenhouse gases. However, for seasonal forecasting the main source of uncertainty is chaotic error growth given possibly very small errors in the initial conditions. Thus these are initial-condition or first-kind, prediction problems, which are quite different from the boundary-condition or second-kind prediction problems in climate prediction.
The present invention is concerned with a method of producing a weather forecast comprising the steps of running an ensemble of coupled atmosphere-ocean global circulation computer models from different initial values, comparing the atmosphere-ocean states predicted by each of the models with a corresponding set of real-world observations, selecting those model states which fit to a predetermined extent the set of observations, and producing a weather forecast from the atmosphere-ocean states subsequently predicted by the selected models.
Thus the present invention lies in applying the “perfect ensemble” approach to the short to medium term forecasting problem. It is expected to be particularly useful for seasonal forecasting. The inventors have found that although the timescales for seasonal forecasting are long, and thus one might expect the perfect ensemble approach (which failed for short-term forecasting) to have even more difficulties on seasonal timescales, in fact the number of important independent degrees of freedom in the initial state of a seasonal forecast is lower than the number of degrees of freedom in a (short-term) atmospheric weather forecast Thus the effective return-time in a seasonal forecasting problem is likely to be relatively short for many variables of interest. This means that a seasonal forecasting model can be run for the equivalent of only centuries of model time to explore the fill range of large-scale ocean-atmosphere states relevant to the seasonal forecasting problem.
With the present invention, therefore, the ensemble members are not, themselves, constrained by direct observations of the present state and evolution of the system, but instead a comparison with observations over an analysis period is used to select and weight members of a sub-ensemble, and the sub-ensemble is then used to make the forecast. The forecast may use a weighted average of trajectories drawn from the ensemble and an estimate of anticipated forecast skill may be provided by the spread of these trajectories.
The set of real-world observations may include observations on the near recent (within one week) state of the atmosphere-ocean system, or the past state of the atmosphere-ocean system over the length of time relevant to the forecast phenomena of interest (this will typically be comparable or longer than the forecast lead time, so data over the past year would be used for six a month forecast).
The set of real-world observations may include observations of the current and past state of the atmosphere-ocean system, such as atmosphere winds, temperatures, pressure, cloud properties, precipitation, surface fluxes, sea level, sea surface temperatures, ocean thermal structure, salinity, soil moisture, vegetation, sea ice and derivatives thereof.
The computer model used may be selected from any suitable model such as the UK Meteorological Office Unified model or the NCAR Community Climate System model. The initial states may be at different points on the climate attractor of the model.
The forecast may be tailored to the requirements of a particular user by interrogating the statistics of the ensemble model simulations to identify skilful predictors under both general and particular regimes. For instance, it may be desired to make a seasonal forecast in relation to only certain aspects of the climate, in which case statistical analysis of the models' output is used to identify which model variables are good predictors for the aspect of the climate of interest, then those models in the ensemble which have the closest match to those predictors are used for the forecast Similarly, one may be interested in a forecast for a particular geographical region, in which case skilful predictors of the weather in that region may be identified, and the models which have the closest match to the current and past values of those predictors are used in the forecast. The forecast may be generated by weighting the contribution made by each of the models in accordance with the closeness of the fit. The fit may be judged by criteria defined by the user. Each user may have a particular threshold for certain weather anomalies, and will select criteria accordingly.
Preferably the models are distributed over a plurality of personal computers. This provides a great deal of computing power. Developments in personal computer technology mean that climate prediction models which formerly would only run on supercomputers, can now be run on a conventional personal computer. Because the vast majority of computer processors, particularly in desk-top personal computers, sit idle for over 90% of the time, a large number of models can be distributed to such personal computers (for instance owned by the general public, or by medium or large organisations) to be run in the otherwise idle time of the computers. Conveniently a client-server arrangement is used in which the server distributes the models to the clients and the clients report back to the server the results of running the model. The models may be left running on the clients, and when it is desired to make a forecast, the server mines the results stored on the personal computers. For instance, the server may cause an additional job to run on each client to identify whether its results to date satisfy the conditions desired for that forecasting problem and thus whether it will be a member of the sub-ensemble. All members of the sub-ensemble then return their subsequent results to the server for the forecast to be generated.
The invention extends to a distributed computing system comprising a server and a plurality of clients as mentioned above, and also to software for distribution to the clients for use in such a distributed computing system.